Updating equations for the error rates
For the updating equations for the error probabilities, we consider a read,![$ i$](img11.gif)
![$ h$](img160.gif)
![$ r_i^h$](img164.gif)
![$ N$](img42.gif)
![$ n_1^h,...,n_{k_h}^h$](img165.gif)
Using Bayes formula again, as we did above in 27.4, we get:
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and inserting the expression from equation 27.7:
The equation 27.9 gives us the probabilities for a given read, , and site,
, given the data
, that the true nucleotide is
,
, given our current values of the error rates and site probabilities. Since we know the sequenced nucleotide in each read at each site, we can get new updated values for the error rate of producing an
nucleotide when the true nucleotide is
,
, for
by summing the probabilities of the true nucleotide being
for all reads across all sites for which the sequenced nucleotide is
, and dividing by the sum of all probabilities of the true nucleotide being a
across all reads and all sites:
![$\displaystyle e^*_q(N \rightarrow M) = \frac{\sum_h \sum_{i=1,...,{k_h}: n_i^h ...
..._{k_h}^h)}{\sum_h \sum_{i=1,...,{k_h}} P(r_i^k = N \vert n_1^h,...,n_{k_h}^h)} $](img181.gif)